






def 					lowerCamelCase__					(_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase):
			global f  # a global dp table for knapsack
			if f[i][j] < 0:
						if j < wt[i - 1]:
									SCREAMING_SNAKE_CASE							=			mf_knapsack(i - 1				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase)
						else:
									SCREAMING_SNAKE_CASE							=			max(
									    mf_knapsack(i - 1				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase)				,							mf_knapsack(i - 1				,							_UpperCAmelCase				,							_UpperCAmelCase				,							j - wt[i - 1]) + val[i - 1]				,							)
						SCREAMING_SNAKE_CASE							=			val
			return f[i][j]






def 					lowerCamelCase__					(_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase):
			SCREAMING_SNAKE_CASE							=			[[0] * (w + 1) for _ in range(n + 1)]

			for i in range(1				,							n + 1):
						for w_ in range(1				,							w + 1):
									if wt[i - 1] <= w_:
												SCREAMING_SNAKE_CASE							=			max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]				,							dp[i - 1][w_])
									else:
												SCREAMING_SNAKE_CASE							=			dp[i - 1][w_]

			return dp[n][w_], dp






def 					lowerCamelCase__					(_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase):
			if not (isinstance(_UpperCAmelCase				,							(list, tuple)) and isinstance(_UpperCAmelCase				,							(list, tuple))):
						raise ValueError(
						    'Both the weights and values vectors must be either lists or tuples')

			SCREAMING_SNAKE_CASE							=			len(_UpperCAmelCase)
			if num_items != len(_UpperCAmelCase):
						SCREAMING_SNAKE_CASE							=			(
						    'The number of weights must be the same as the number of values.\n'
						    F'''But got {num_items} weights and {len(_UpperCAmelCase)} values'''
						)
						raise ValueError(_UpperCAmelCase)
			for i in range(_UpperCAmelCase):
						if not isinstance(wt[i]				,							_UpperCAmelCase):
									SCREAMING_SNAKE_CASE							=			(
									    'All weights must be integers but got weight of '
									    F'''type {type(wt[i])} at index {i}'''
									)
									raise TypeError(_UpperCAmelCase)

			SCREAMING_SNAKE_CASE					,    SCREAMING_SNAKE_CASE							=			knapsack(_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase)
			SCREAMING_SNAKE_CASE							=			set()
			_construct_solution(_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase)

			return optimal_val, example_optional_set






def 					lowerCamelCase__					(_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase				,							_UpperCAmelCase):
			# for the current item i at a maximum weight j to be part of an optimal subset,
			# the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
			# where i - 1 means considering only the previous items at the given maximum weight
			if i > 0 and j > 0:
						if dp[i - 1][j] == dp[i][j]:
									_construct_solution(_UpperCAmelCase				,							_UpperCAmelCase				,							i - 1				,							_UpperCAmelCase				,							_UpperCAmelCase)
						else:
									optimal_set.add(_UpperCAmelCase)
									_construct_solution(_UpperCAmelCase				,							_UpperCAmelCase				,							i - 1				,							j - wt[i - 1]				,							_UpperCAmelCase)


if __name__ == "__main__":
				a_		:    int   							=     [3, 2, 4, 4]
				a_		:    Union[str, Any]   							=     [4, 3, 2, 3]
				a_		:    Tuple   							=     4
				a_		:    Optional[int]   							=     6
				a_		:    Dict   							=     [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
				a_							,       a_		:    str   							=     knapsack(w, wt, val, n)
				print(optimal_solution)
				print(mf_knapsack(n, wt, val, w))  # switched the n and w

				# testing the dynamic programming problem with example
				# the optimal subset for the above example are items 3 and 4
				a_							,       a_		:    Union[str, Any]   							=     knapsack_with_example_solution(w, wt, val)
				assert optimal_solution == 8
				assert optimal_subset == {3, 4}
				print('optimal_value = ', optimal_solution)
				print('An optimal subset corresponding to the optimal value', optimal_subset)





from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import ScoreSdeVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput




class   _UpperCamelCase (		_UpperCAmelCase					):


			"""simple docstring"""






			__a    :					UNetaDModel
			__a    :					ScoreSdeVeScheduler





			def __init__(  self ,  lowerCAmelCase__ ,  lowerCAmelCase__		)	->   Union[str, Any]:

							'''simple docstring'''


							super().__init__()
							self.register_modules(unet=lowerCAmelCase__ ,  scheduler=lowerCAmelCase__		)





			@torch.no_grad()
			def __call__(  self ,  lowerCAmelCase__ = 1 ,  lowerCAmelCase__ = 20_00 ,  lowerCAmelCase__ = None ,  lowerCAmelCase__ = "pil" ,  lowerCAmelCase__ = True ,  **lowerCAmelCase__ ,  )	->   Union[ImagePipelineOutput, Tuple]:

							'''simple docstring'''


							__lowercase					     =				self.unet.config.sample_size
							__lowercase					     =				(batch_size, 3, img_size, img_size)

							__lowercase					     =				self.unet

							__lowercase					     =				randn_tensor(lowerCAmelCase__ ,  generator=lowerCAmelCase__		) * self.scheduler.init_noise_sigma
							__lowercase					     =				sample.to(self.device		)

							self.scheduler.set_timesteps(lowerCAmelCase__		)
							self.scheduler.set_sigmas(lowerCAmelCase__		)

							for i, t in enumerate(self.progress_bar(self.scheduler.timesteps		)		):
											__lowercase					     =				self.scheduler.sigmas[i] * torch.ones(shape[0] ,  device=self.device		)

											# correction step
											for _ in range(self.scheduler.config.correct_steps		):
															__lowercase					     =				self.unet(lowerCAmelCase__ ,  lowerCAmelCase__		).sample
															__lowercase					     =				self.scheduler.step_correct(lowerCAmelCase__ ,  lowerCAmelCase__ ,  generator=lowerCAmelCase__		).prev_sample

											# prediction step
											__lowercase					     =				model(lowerCAmelCase__ ,  lowerCAmelCase__		).sample
											__lowercase					     =				self.scheduler.step_pred(lowerCAmelCase__ ,  lowerCAmelCase__ ,  lowerCAmelCase__ ,  generator=lowerCAmelCase__		)

											__lowercase     ,	__lowercase					     =				output.prev_sample, output.prev_sample_mean

							__lowercase					     =				sample_mean.clamp(0 ,  1		)
							__lowercase					     =				sample.cpu().permute(0 ,  2 ,  3 ,  1		).numpy()
							if output_type == "pil":
											__lowercase					     =				self.numpy_to_pil(lowerCAmelCase__		)

							if not return_dict:
											return (sample,)

							return ImagePipelineOutput(images=lowerCAmelCase__		)